ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 43, 44 Sakakibara, Nobuhisa, Faculty of Engineering, Ibaraki University, Japan Perfectness of conelike ∗-semigroups in Q^{k} Let S be an abelian ∗-semigroup in Q^{k}. We give a sufficient condition for every positive definite function on S to have a unique representing measure on the dual semigroup of S (i. e. S is perfect). To characterize perfectness for any abelian ∗-semigroup is a challenging, but not yet generally solved problem. In this talk, we characterize the structure of involutions on an abelian ∗-semigroup which is a subset of Q^{k}, and show that all conelike ∗-semigroups in Q^{k} are perfect.